The square-transform of Hermite-Biehler functions. A geometric approach

Abstract

We investigate the subclass of symmetric indefinite Hermite-Biehler functions which is obtained from positive definite Hermite-Biehler functions by means of the square-transform. It is known that functions of this class can be characterized in terms of location of their zeros. We give another, more elementary and geometric, proof of this result. The present proof employs a `shifting-of-zeros' perturbation method. We apply our results to obtain information on the eigenvalues of a concrete boundary value problems.

Full Text

Article Information

Title	The square-transform of Hermite-Biehler functions. A geometric approach
Source	Methods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 187-200
MathSciNet	MR2336721
Copyright	The Author(s) 2007 (CC BY-SA)

Authors Information

Vyacheslav Pivovarchik
Department of Applied Mathematics and Informatics, South-Ukrainian State Pedagogical University, 26, Staroportofrankovskaya, Odessa, UA-65091, Ukraine

Harald Woracek
Departement for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10/101, A-1040 Wien, Austria 

Citation Example

Vyacheslav Pivovarchik and Harald Woracek, The square-transform of Hermite-Biehler functions. A geometric approach, Methods Funct. Anal. Topology 13 (2007), no. 2, 187-200.

BibTex

@article {MFAT405,
    AUTHOR = {Pivovarchik, Vyacheslav and Woracek, Harald},
     TITLE = {The square-transform of Hermite-Biehler functions. A geometric approach},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {187-200},
      ISSN = {1029-3531},
  MRNUMBER = {MR2336721},
       URL = {http://mfat.imath.kiev.ua/article/?id=405},
}